On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed wave-following coordinate system. Part 2

Abstract

This experimental study extends our earlier work (Hsu, Hsu & Street 1981) on U∞/c = 1.54 to U∞/c = 0.88, 1.10, 1.36 and 1.87, where U∞ is the mean-free-stream wind velocity and c is the celerity of the water wave. This was accomplished by changing the speed of the turbulent wind, while the water wave was maintained at a frequency of 1.0 Hz and wave slope of 0.1. The consistency between the results of the present and earlier experiments is established. The experimental results indicate that the mean velocity of the typical log-linear profile basically follows the waveform. However, the surface condition for the wind is regarded as supersmooth because the mean turbulent shear stress supported by the current is relatively lower than that supported by a smooth flat plate. The structure of the wave-induced velocity fields is found to be very sensitive to the height of the critical layer. When the critical height is high enough that most of the wave-induced flow in the turbulent boundary layer is below the critical layer, the structure of the wave-induced velocity field is strongly affected by the Stokes layer, which under the influence of the turbulence can have thickness comparable to the boundary-layer thickness. When the critical height is low enough that most of the wave-induced flow in the boundary layer is above the critical layer, the structure of the wave-induced velocity fields is then strongly affected by the critical layer. The structure of the critical layer is found to be nonlinear and turbulently diffusive. This implies that the inclusion of both the nonlinear and the turbulent terms in the wave-perturbed momentum equations is essential to success in the numerical modelling. The response of the turbulent Reynolds stresses to the wave is found to depend on the flow regimes near the interface or in the boundary layer. Near the interface, the wave-induced turbulent Reynolds stresses are found to be produced mainly from the stretching and changing in the direction of the turbulent velocity fluctuations due to the surface displacements. In the boundary layer, the eddy-viscosity-type relation between the wave-induced turbulent Reynolds stresses and the wave-induced velocities as found in Hsu et al. (1981) for U∞/c = 1.54 is also found to hold for the other U∞/c values of this study.